8 citations · 13 across the 7 of their papers we have counts for
7 papers
Eisenstein circle packings and the Eisenpint Schmidt arrangement
James Rickards, Katherine E. Stange
The Schmidt arrangement of an imaginary quadratic number field is the orbit of the extended real line under as Möbius transformations on the exte…
The local-global conjecture for Apollonian circle packings is false
Summer Haag, Clyde Kertzer, James Rickards +1
In a primitive integral Apollonian circle packing, the curvatures that appear must fall into one of six or eight residue classes modulo 24. The local-global conjecture states that…
Linking number of modular knots
James Rickards
We compute the linking number of two modular knots in the space with the trefoil filled in, which answers a question…
The Apollonian staircase
James Rickards
A circle of curvature is a part of finitely many primitive integral Apollonian circle packings. Each such packing has a circle of minimal curvature , a…
Improved computation of fundamental domains for arithmetic Fuchsian groups
James Rickards
A practical algorithm to compute the fundamental domain of an arithmetic Fuchsian group was given by Voight, and implemented in Magma. It was later expanded by Page to the case of…
Hecke operators acting on optimal embeddings in indefinite quaternion algebras
James Rickards
We explore a natural action of Hecke operators acting on formal sums of optimal embeddings of real quadratic orders into Eichler orders. By associating an optimal embedding to its…
Counting intersection numbers of closed geodesics on Shimura curves
James Rickards
Let correspond to the group of units of norm in an Eichler order of an indefinite quaternion algebra over . Close…